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sec
2
θ
=
1
+
tan
2
θ
{\displaystyle \sec ^{2}\theta =1+\tan ^{2}\theta }
0
=
tan
θ
Δ
x
−
Δ
y
+
4.9
(
Δ
x
v
cos
θ
)
2
{\displaystyle 0=\tan \theta \Delta x-\Delta y+4.9\left({\frac {\Delta x}{v\cos \theta }}\right)^{2}}
0
=
tan
θ
Δ
x
−
Δ
y
+
4.9
(
1
+
tan
2
θ
)
(
Δ
x
v
)
2
{\displaystyle 0=\tan \theta \Delta x-\Delta y+4.9(1+\tan ^{2}\theta )\left({\frac {\Delta x}{v}}\right)^{2}}
tan
θ
=
Δ
x
±
Δ
x
2
−
96.04
(
Δ
x
v
)
2
(
(
Δ
x
v
)
2
−
Δ
y
)
9.8
(
Δ
x
v
)
2
{\displaystyle \tan \theta ={\frac {\Delta x\pm {\sqrt {\Delta x^{2}-96.04\left({\frac {\Delta x}{v}}\right)^{2}(\left({\frac {\Delta x}{v}}\right)^{2}-\Delta y)}}}{9.8\left({\frac {\Delta x}{v}}\right)^{2}}}}
tan
θ
=
Δ
x
±
Δ
x
1
−
96.04
(
1
v
)
2
(
(
Δ
x
v
)
2
−
Δ
y
)
9.8
(
Δ
x
v
)
2
{\displaystyle \tan \theta ={\frac {\Delta x\pm \Delta x{\sqrt {1-96.04\left({\frac {1}{v}}\right)^{2}(\left({\frac {\Delta x}{v}}\right)^{2}-\Delta y)}}}{9.8\left({\frac {\Delta x}{v}}\right)^{2}}}}
tan
θ
=
v
2
1
±
1
−
96.04
(
1
v
)
2
(
(
Δ
x
v
)
2
−
Δ
y
)
9.8
Δ
x
{\displaystyle \tan \theta =v^{2}{\frac {1\pm {\sqrt {1-96.04\left({\frac {1}{v}}\right)^{2}(\left({\frac {\Delta x}{v}}\right)^{2}-\Delta y)}}}{9.8\Delta x}}}
θ
=
arctan
(
v
2
1
±
1
−
96.04
(
1
v
)
2
(
(
Δ
x
v
)
2
−
Δ
y
)
9.8
Δ
x
)
{\displaystyle \theta =\arctan \left(v^{2}{\frac {1\pm {\sqrt {1-96.04\left({\frac {1}{v}}\right)^{2}(\left({\frac {\Delta x}{v}}\right)^{2}-\Delta y)}}}{9.8\Delta x}}\right)}
